A conventional ultrasound imaging system includes an array of ultrasonic transducers that transmit an ultrasound wave (a transient pressure wave) during a transmit mode and receive a reflected wave reflected from an object under study during a receive mode. The spatial response to this ultrasound wave is referred to as an ultrasound beam. In general, the overall (two-way) beam is a combination of two separate beams: a transmit beam, which represents the degree to which energy is deposited in the object, and a receive beam, which represents a system response to echoes originating at various points in space. The signals generated by the transducers responsive to the received pressure wave are processed and the results displayed as a visual image of the object.
The array typically includes a multiplicity of transducers configured as a linear array or row, each transducer driven by a separate signal voltage during the transmit mode. Selecting a time delay (relative to a reference time) for the signal voltage applied to each transducer controls a direction of the ultrasonic beam energy transmitted by the individual transducers. In addition, controlling the amplitude of the signal voltage applied to each transducer can be used to lower energy present in sidelobes of the ultrasound beam.
Controlling the time delay steers the ultrasonic energy emitted by the transducers to produce a net ultrasonic wave that travels along (scans) the object in a desired direction or along a scan line (also referred to as an A-line), with the energy focused at a selected point on the scan line. That is, the transmit energy is focused or concentrated at a fixed range (fixed focal point) from the transducer array, maximally localizing the energy at that range. At other ranges (distances from the transducer array) the energy is localized to a lesser extent, producing a broader beam. Thus although the energy is focused at only a single point on the scan line, the energy at proximate points (the points comprising a focal zone) may be sufficient to produce a reflected beam that can be processed to render an image with sufficient lateral resolution.
Similar beam-combining principles are employed when the transducers receive the reflected ultrasonic energy from the scan line. The voltages produced at the receiving transducers are controllably delayed and summed so that the net received signal response is primarily representative of the ultrasonic energy reflected from a single focal zone along the scan line of the object.
To generate a two dimensional or planar image of the object (and recognizing that ultrasound imaging occurs in the near field), during the receive mode the transducers are dynamically focused at successive ranges from the transducer array (depths into the object being scanned) along the scan line as the reflected ultrasonic waves are received. The focused range is based on the round-trip travel time of the ultrasound pulse. Controlling the time-delay associated with each transducer focuses the received energy at the desired time-variant range or depth. Such dynamic focusing in the receive mode produces a usable response at the focal point and a range of distances near the focal point. The range over which the two-way response of the system is well-focused is referred to as the depth of field. Outside the depth of field the image quality suffers and the reflections are not usable to produce the image.
As can be appreciated, the instantaneous beam steering and signal combining capabilities of the linear transducer array are capable of producing only a 2D image of the object, where the image is in the plane normal to the array surface and contains the centers of the array elements.
Deformable models are known in the art and were first used in computer animation to produce realistic motion of an elastic object. A deformable model models elastic object surfaces using connected mass elements according to various physics-based or geometric techniques. As illustrated in FIG. 1, an object surface 8 is modeled as grids of point masses 10. Each mass is connected to one or more adjacent masses by a rigid elastic rod 12 that exerts a return force on the connected masses when bent, stretched or compressed away from its rest state. Different masses can also be connected by other exemplary connecting rods.
The dynamics of the surface 8 can be defined at each mass by a force balance equation such as:
                              m          ⁢                                          ⁢                      x            ¨                          +                  k          ⁢                                          ⁢                      x            .                                      ︸                                                            forces                ⁢                                                                  ⁢                from                                                                                        object                ⁢                                                                  ⁢                dynamics                                                          +                  δ        ⁢                                  ⁢                  E          ⁡                      (            x            )                                      ︸                                            internal                                                          force                                            =            f      user              ︸                                    external                                                force                              where x is a position vector of the masses, m is the mass of each point or particle, k is a viscous friction constant (often assumed to be zero) and the variational symbol δE(x) is a restoring force proportional to the local curvature of the surface at the location of the point mass. The dots represent vector component-wise time derivatives. The variable x and the x-dot variables are vectors in a three dimensional space that describe the instantaneous condition (location, velocity, acceleration, etc.) of the model at any instant in time. State equations defining the deformable model are derived from the force balance equation and consist of state variables and their derivatives.
The force balance equation depicts the balance of forces resulting from motion of the point masses (forces based on the object dynamics), restoring forces arising from the curvature of the surface at the location of the point mass and external forces controlling motion of the modeled object. For the computer animation application, external forces are specified by the animator.
For medical image analysis, the external forces are represented by a potential field that is derived from the acoustic echoes that form the image. Strong image echoes form a strong potential field and weak image echoes (dark regions of the image) form a weak potential field. The echo magnitude and the potential field derived from it can be regarded as a type of charge attracting oppositely charged point masses of the object. The model masses are therefore attracted to the strong potential field regions, causing the model to conform to the image. The model masses are only weakly attracted to the weak potential field derived form the weak image echoes.
When a deformable model is used for static segmentation of a still image in the prior art, the external forces responsive to the potential field are generally more important than the dynamics of the model's surface. Application of the deformable model to the static segmentation application requires only that the model's final configuration represent an equilibrium position of the surface in the external potential field generated by the image. The model's transient response can be any response that is convenient to the model designer. The fastest static model response occurs when the model points have very low mass, minimizing the effects of object dynamics. (This type of response also eliminates overshoot and the resulting oscillations that can occur in linear systems. Such oscillations tend to slow the model's response to the potential field.)
In effect, the deformable model, absent consideration of the object's dynamics, is a method for managing a constrained optimal fit of the model to the image. The constraint is a smoothness constraint and is represented by the elastic return forces of the model. The objective function is a measure of the fit of the model to the image and is represented by the potential energy field as derived from the image. This technique can also be applied to tracking a moving surface using a sequence of complete images, since every image can be fit separately using constraints derived from images taken at about the same time to ensure a smooth evolution of the model shape through the image sequence.
The model set forth in the equation above allows the state variables (e.g., acceleration, velocity and position of the masses) to evolve in response to the various forces that act on them. This evolution is simulated by a discrete-time computational process in which the continuous-time state transition matrix associated with the equations of motion above is integrated to form a discrete time system matrix. Each time a multiplication of the state vector by this matrix is performed, new external force information can be incorporated into the computation as a discrete time driving function. The details of such discrete time systems are well known. For example, consult Digital Control of Dynamic Systems, by G. F. Franklin and J. D. Powell (Addison Wesley, 1980).